In a large bowl, combine the mustard, vinegar, 2 tablespoons of the oil, the garlic, tarragon, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add the chicken and toss to coat. Place the chicken in a roasting pan and roast until cooked through, about 45 minutes.
During the last 15 minutes of roasting, cook the noodles according to the package directions. Drain and return to the pot. Add the parsley and the remaining oil and toss to coat.
Transfer the chicken to individual plates. Place the pan containing the drippings over medium-high heat. Add the wine and cook, stirring and scraping the bits from the bottom of the pan, until the wine reduces slightly, about 5 minutes.
Divide the noodles among the plates and spoon the sauce over the top.